Ah, I think I understand Mr Frog's point.
Let's assume that a roller can accelerate a minecart to 20/s in the direction it's built, if the minecart fully traverses the roller.
This happens after the initial wall-slam.
2: Cart passes over the roller, robbing it of some momentum before it hits the wall and stops.
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====0#
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The cart passes the roller, being decelerated and hitting the wall afterwards.
At this point, v= 0/s.
3: The roller applies force, sending the cart from the right, to the left.
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==0=<#
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Now it gains momentum. Its mass remains the same (if minecarts don't reach relativistic speeds, which we'll assume for now), so it's sufficient to observe the velocities.
The cart fully traverses the roller and is accelerated to v=20/s.
4: This is actually ping-pong.
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It's not quite ping-pong, and the cause is friction.
The minecart loses a bit of its speed, so it arrives at the second roller with less than 20/s, maybe 18/s.
The moment it moves on the roller, it's getting decelerated. Now, if a roller can accelerate a minecart to 20/s, it can also decelerate a minecart with 20/s to 0/s if it fully traverses the roller in the opposite direction. The problem here is: our minecart is slower than 20/s. As a result, it cannot reach the other side of the roller because the roller decelerates it too much. The cart cannot slam into the wall, and it stops somewhere on the roller (2/20 of a tile off the wall, to be exact).
Because it can't fully traverse the roller, it won't get accelerated to -20/s, only to -18/s again. The trend here is obvious: the cart will lose some of its velocity again, acceleration won't suffice etc.
Long story short, the cart will stop in the middle eventually.
That is, if Mr Frog's conception of a roller is correct (and I think it's likely)
(and if I understood it correctly).
This post was brought to you by the verb: to traverse.